When dd1 was little she demanded her bassinet(then later crib). DD2 could always sleep where ever. When she was around 12mos I did start putting her in her crib around the same time everyday to get on dd1's nap schedule. My kids ALWAYS slept on their backs until they could roll themselves over.

DS napped on me or in his swing until 3-4 months old (both of them). Then we transitioned to his crib. He slept on his back until he learned to roll over, now is in all sorts of positions throughout his nap/sleep. Right now he's on his side (video monitor).